Mathematics, Volume 12, Issue 1

Deep learning technology has greatly propelled the development of intelligent and information-driven research on ship infrared automatic target recognition (SIATR). In future scenarios, there will be various recognition models with different mechanis...

Difference schemes that approximate dynamic systems are considered discrete models of the same phenomena that are described by continuous dynamic systems. Difference schemes with t-symmetry and midpoint and trapezoid schemes are considered. It is sho...

In this paper, we establish the cohomology of relative Rota–Baxter operators on Lie-Yamaguti algebras via the Yamaguti cohomology. Then, we use this type of cohomology to characterize deformations of relative Rota–Baxter operators on Lie-...

The article is devoted to the analytical and numerical study of the pattern of propagation and attenuation, due to Coulomb friction, of shear waves in an infinite elastic thin plate with a circular orifice of radius $r_0$ lying on a rough base. Consider...

At present, sequence-based models have various applications in recommendation systems; these models recommend the interested items of the user according to the user’s behavioral sequence. However, sequence-based models have a limitation of leng...

In this paper, the distributed interval estimation problem for networked Cyber-Physical systems suffering from both disturbances and noise is investigated. In the distributed interval observers, there are some connected interval observers built for t...

Partially linear models find extensive application in biometrics, econometrics, social sciences, and various other fields due to their versatility in accommodating both parametric and nonparametric elements. This study aims to establish statistical i...

We model the spatiotemporal dynamics of a community consisting of competing weed and cultivated plant species and a population of specialized phytophagous insects used as the weed biocontrol agent. The model is formulated as a PDE system of taxis&nda...

Real-time evaluation of the damage location and level of rock mass is essential for preventing underground engineering disasters. However, the heterogeneity of rock mass, which results from the presence of layered rock media, faults, and pores, makes...

Ill-posed problems arise in many areas of science and engineering. Tikhonov is a usual regularization which replaces the original problem by a minimization problem with a fidelity term and a regularization term. In this paper, a tensor t-production s...

In this paper, we applied a chaos control method based on integro-differential equations for stabilization of an unstable cardiac rhythm, which is described by a variation of the modified Van der Pol equation. Chaos control with this method may be us...

We define and study enriched Suzuki mappings in Hadamard spaces. The results obtained here are extending fundamental findings previously established in related research. The extension is realized with respect to at least two different aspects: the se...

This article presents an extended distribution that builds upon the exponential distribution. This extension is based on a scale mixture between the exponential and beta distributions. By utilizing this approach, we obtain a distribution that offers...

This paper focuses on the asymptotic behavior of nonautonomous neural networks with delays. We establish criteria for analyzing the asymptotic behavior of nonautonomous recurrent neural networks with delays by means of constructing some new generaliz...

Since its introduction in 1650, Kepler’s equation has never ceased to fascinate mathematicians, scientists, and engineers. Over the course of five centuries, a large number of different solution strategies have been devised and implemented. Amo...

The fusion of camera and LiDAR perception has become a research focal point in the autonomous driving field. Existing image–point cloud fusion algorithms are overly complex, and processing large amounts of 3D LiDAR point cloud data requires hig...

In this paper, an intelligent weather conditions fuzzy adjustment based on spatial features (IWeCASF) is developed. It is indispensable for our regional soil moisture estimation approach, complementing a point estimation model of soil moisture from t...

This paper primarily focuses on the chaos synchronisation analysis of neural networks (NNs) under a hybrid controller. Firstly, we design a suitable hybrid controller with saturated impulse control, combined with time-dependent intermittent control....

A distributed-power-generating source (DPGS) is intended to locally supply the increased power demand at a load bus. When applied in small amounts, a DPGS offers many technical and economic benefits. However, with large DPGS penetrations, the stabili...

Dependent random variables play a crucial role in various fields, from finance and statistics to engineering and environmental sciences. Often, interest lies in understanding the aggregate sum of a collection of dependent variables with random weight...

Dealing with municipal sludge in an effective way is crucial for urban development and environmental protection. Co-processing the sludge by burning it in a decomposition furnace in the cement production line has been found to be a viable solution. T...

Based on the published papers in this Special Issue of the elite scientific journal Mathematics, we herein present the Editorial for “Differential Equations of Mathematical Physics and Related Problems of Mechanics”, the main topics of wh...

We introduce De Morgan Heyting logic for Heyting algebras with De Morgan negation (DH-algebras). The variety $\mathcal{DH}$ of all DH-algebras is congruence distributive. The lattice of all subvarieties of $\mathcal{DH}$ is distributive. We show the discrete dualities betwe...

This paper theoretically investigates the influence of homo- and hetero-junctions on the propagation characteristics of radially propagated cylindrical surface acoustic waves in a piezoelectric semiconductor semi-infinite medium. First, the basic equ...

We continue studying the $\sigma$-Ricci vector field $\mathbf{u}$ on a Riemannian manifold $(N^m,g)$, which is not necessarily closed. A Riemannian manifold with Ricci operator T, a Coddazi-type tensor, is called a T-manifold. In the first result of this paper, we...

We extend existing functional relationships for the discrete generating series associated with a single-variable linear polynomial coefficient difference equation to the multivariable case.

As part of the research in the recently ended project SANET II, we were trying to create a new machine-learning system without a teacher. This system was designed to recognize DDoS attacks in real time, based on adaptation to real-time arbitrary traf...

LIDAR is central to the perception systems of autonomous vehicles, but its performance is sensitive to adverse weather. An object detector trained by deep learning with the LIDAR point clouds in clear weather is not able to achieve satisfactory accur...

Statistical mechanics of walks defined on the spatial graphs of the city of Lubbock (10,421 nodes) and the Texas Tech University (TTU) campus pedestrian network (1466 nodes) are used for evaluating structural isolation and the integration of graph no...

In recent years, the economies of many countries around the world have been in a situation of intense, rapidly changing, abrupt processes. The current situation urgently requires a change in the economic paradigm in the near future, which leads to th...

The study of differential equation theory has come a long way, with applications in various fields. In 1961, Zygmund and Calderón introduced the notion of derivatives to metric $L^r$, which proved to be better in applications than approximate der...

This paper proposes a Kalman filter for linear rectangular singular discrete-time systems, where the singular matrix in the system is a rectangular matrix without full column rank. By using two different restricted equivalent transformation methods a...

In this article, we introduce a new continuous distribution based on the unit interval. This distribution is generated from a transformation of a random variable with half-normal distribution. We study its basic properties, percentiles, moments and o...

In this paper, the adaptive consensus problem of unknown non-linear multi-agent systems (MAs) with communication noises under Markov switching topologies is studied. Based on the adaptive control theory, a novel distributed control protocol for non-l...

Most research on malware focuses mainly on its detection, without paying attention to its propagation trends. However, modeling the spread of malware is an important research problem because it allows us to predict how malware will evolve and to take...

Power system operation mode calculation (OMC) is the basis for unit commitment, scheduling arrangement, and stability analyses. In dispatch centers at all levels, OMC is usually realized by manually adjusting the parameters of power system components...

In the information age, frequent information exchange has provided a breeding ground for the spread of computer viruses. The significant losses caused by computer virus attacks have long rung the alarm for information security. From academia to busin...

We consider two abstract systems of parabolic–hyperbolic type that model thermoelastic problems. We study the influence of the physical constants and the initial data on the nonexistence of global solutions that, in our framework, are produced...

Microseismic P- and S-phase segmentation is an influential step that limits the accuracy of event location, parameter inversion, and mechanism analysis. Therefore, an improved Unet named PSSegNet is proposed to intelligently segment the P- and S-phas...

The Feynman–Kac formula establishes a link between parabolic partial differential equations and stochastic processes in the context of the Schrödinger equation in quantum mechanics. Specifically, the formula provides a solution to the part...

This is a noticeably short biography and introductory paper on multiplier Hopf algebras. It delves into questions regarding the significance of this abstract construction and the motivation behind its creation. It also concerns quantum linear groups,...

The convergence theorems play an important role in the theory of probability and statistics and in its application. In recent times, we studied three types of convergence of intuitionistic fuzzy observables, i.e., convergence in distribution, converg...

Let ${\left(k_{\mu }\right)}_{\mu =1}^4$ be a quartet of cyclic cubic number fields sharing a common conductor $c=pqr$ divisible by exactly three prime(power)s, $p,q,r$. For those components of the quartet whose 3-class group ${\mathrm{Cl}}_3\left(k_{\mu }\right)\simeq {(\mathbb{Z}/3\mathbb{Z})}^2$ is elementary bicyclic, t...

We demonstrate a basic technique for simplifying time-periodic competition models, which is based on the utilization of periodic delta functions as population growth rates. We show that the Poincare mapping splits into a sequence of one-dimensional m...

Vehicle detection is crucial for traffic surveillance and assisted driving. To overcome the loss of efficiency, accuracy, and stability in low-light conditions, we propose a lightweight “You Only Look Once” (YOLO) detection model. A polar...

In this study, we consider a system of nonlinear differential equations modeling the human immunodeficiency virus type-1 (HIV-1) in a variable environment. Infected cells were subdivided into two compartments describing both latently and productively...

In the context of the burgeoning cloud-edge collaboration paradigm, powered by advancements in the Internet of Things (IoT), cloud computing, and 5G technology, this paper proposes a task orchestrating strategy for cloud-edge collaborative environmen...

In this scholarly discourse, we present proof of the existence of unique fixed points in b-metric spaces for hybrid rational contractions. Moreover, we establish a common fixed point theorem for four self-mappings, assuming S-compatibility for two pa...

Nonstationary fuzzy inference systems (NFIS) are able to tackle uncertainties and avoid the difficulty of type-reduction operation. Combining NFIS and neural network, a first-order sparse TSK nonstationary fuzzy neural network (SNFNN-1) is proposed i...

Disability management in information systems refers to the process of ensuring that digital technologies and applications are designed to be accessible and usable by individuals with disabilities. Traditional methods face several challenges such as p...